Question: The following line passes through point $(-9, 8)$ : $y = -\dfrac{3}{4} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-9, 8)$ into the equation gives: $8 = -\dfrac{3}{4} \cdot -9 + b$ $8 = \dfrac{27}{4} + b$ $b = 8 - \dfrac{27}{4}$ $b = \dfrac{5}{4}$ Plugging in $\dfrac{5}{4}$ for $b$, we get $y = -\dfrac{3}{4} x + \dfrac{5}{4}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-9, 8)$